Changing a dimension always immediately resets to 0
Dimensions work as a scale multiplier. As your mesh has a Y dimension of 0, you can multiply it by any number, the result will always be 0.
To get thickness you need to enter edit mode, select all and press E to extrude the faces.
Once the object has Y dimension different than 0 you will be able to vary it in the N panel.
Be aware that you have the snap option activated.